Application of continuous-discrete unscented Kalman filter for control of nonlinear systems with actuator nonlinearity

Actuator nonlinearity exists in many physical systems and devices such as piezoelectric actuators, electronic relay circuits, smart materials, etc. In this paper, we consider control of stochastic system with actuator nonlinearity. We use existing adaptive controller including parameter update law and control law, which can achieve exponential tracking of a class of nonlinear deterministic system. However, the controller cannot be practically applied since the presence of observation noise leads to the divergence of parameter update law. Furthermore, the sensitivity of the control law signal induces bursting behavior which may, in practice, damage actuators. We modify both the parameter update law and the control law to avoid divergence and reduce the sensitivity. In addition, we use continuous-discrete unscented Kalman filter to estimate state and unknown parameters of the system. The effectiveness of our proposed control method is clarified by a numerical example of a second order dynamical system with dead-zone nonlinearity.